Explanation Given Information: The values of f ( x ) for different values x : f ( − 1 ) = 5 , f ( 1 ) = 3 , f ( 2 ) = 5 Calculation: To obtain the quadratic function at first we will find the coefficients a, b, c . Since, f ( x ) = a x 2 + b x + c . So, f ( − 1 ) = 5 gives, f ( − 1 ) = a ( − 1 ) 2 + b ( − 1 ) + c 5 = a − b + c a − b + c = 5 (I) f ( 1 ) = 3 gives, f ( 1 ) = a ( 1 ) 2 + b ( 1 ) + c 3 = a + b + c a + b + c = 3 (II) f ( 2 ) = 5 gives, f ( 2 ) = a ( 2 ) 2 + b ( 2 ) + c 5 = 4 a + 2 b + c 4 a + 2 b + c = 5 (III) Equations (I), (II) and (III) give, a − b + c = 5 a + b + c = 3 4 a + 2 b + c = 5 Use the Gauss elimination method to obtain the solution of the above system of equation. The matrix corresponding to the system of equation is as follows: [ 1 − 1 1 5 1 1 1 3 4 2 1 5 ] The matrix will be converted into the echelon form by using the elementary row transformation

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ISBN: 9780134469140

Author: Robert F. Blitzer

Publisher: PEARSON

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Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.

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Chapter 8.1, Problem 40PE

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To calculate: The quadratic function f(x)=ax2+bx+c where f(−1)=5,f(1)=3,f(2)=5.

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Chapter 8.1, Problem 39PE

Chapter 8.1, Problem 41PE

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Chapter 8 Solutions

Precalculus (6th Edition)

Ch. 8.1 - Check Point 1 Write the augmented matrix for the...Ch. 8.1 - Check Point 2 Use the matrix ...Ch. 8.1 - Check Point 3 Use matrices to solve the system:...Ch. 8.1 - Check Point 4 Use matrices to solve the system:...Ch. 8.1 - Check Point 5 Solve the system in Check Point. 3...Ch. 8.1 - Prob. 1CVC Ch. 8.1 - Fill in each blank so that the resulting statement...Ch. 8.1 - Prob. 3CVC Ch. 8.1 - Prob. 4CVC Ch. 8.1 - Fill in each blank so that the resulting statement...

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The quadratic function f ( x ) = a x 2 + b x + c where f ( − 1 ) = 5 , f ( 1 ) = 3 , f ( 2 ) = 5 .

Solution Summary: The author explains how to calculate the quadratic function f(x) = ax 2+bx+c.

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To calculate: The quadratic function f(x)=ax2+bx+c where f(−1)=5,f(1)=3,f(2)=5.

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Chapter 8 Solutions